GBS operators of Schurer-Stancu type
|
|
- Debra Horton
- 5 years ago
- Views:
Transcription
1 Annals of University of Craiova, Math. Comp. Sci. Ser. Volume 30, 003, Pages ISSN: GBS operators of Schurer-Stancu type Dan Bărbosu In the memory of Professor E. Dobrescu Abstract. If p 0,q 0 are given positive integers and α 1,β 1,α,β are real parameters satisfying 0 α 1 β 1,0 α β, in [9] was constructed the bivariate Schurer- Stancu operator S α 1,β 1,α,β : C[0, 1+p] [0, 1+q] C[0, 1] [0, 1] defined for any f C[0, 1+p] [0, 1+q] and any m, n N by Sα 1,β 1,α,β f x, y = = m+p n+q k + p α1 mkx p nj yf, j + α k=0 j=0 m + β 1 n + β where p m,k n, p nj y are the fundamental Schurer polynomials and approximation properties of this operator were established. Denoting by C b [0, 1+p] [0, 1+q] the space of B-continuous real valued functions defined on [0, 1+p] [0, 1+q] the GBS operator associated to S α 1,β 1,α,β is constructed. This operator, denoted by Ũ α 1,β 1,α,β applies the space C b [0, 1+p] [0, 1+q] into C b [0, 1] [0, 1] and it is defined for any f C b [0, 1+p] [0, 1+q] and any m, n N by α Ũ 1,β 1,p 1,q 1 f x, y = m n p m,kx p nj y k=0 j=0 {fk/m, y+fx, j/n fk/m, j/n Some approximation properties concerning a convergence theorem and the approximation α order, in terms of mixed modulus of smoothness, for the sequence {Ũ 1,β 1,α,β f m,n N are established. Note that for p = q =0andα 1 = β 1 = α = β = 0 our GBS operator reduces to the GBS operator of Bernstein type, constructed in 1966 by E. Dobrescu and I. Matei [15]. The paper is devoted to the memory of the GREAT Romanian Mathematician, Professor Eugen Dobrescu, disappeared premature in Mathematics Subject Classification. 41A36, 41A63. Key words and phrases. positive linear operator, Bernstein operator, Schurer operator, Stancu operator, B-continuous function, parametric extension, GBS operator, mixed modulus of smoothness. 1. Preliminaries Let p 0 be a given integer. In 196 F. Schurer see [18] constructed and studied the positive and linear operator Bm,p : C[0, 1 + p] C[0, 1], which associates to any function f C[0, 1 + p] the polynomial B m,p f defined by Bm,p f x, y = m+p k=0 p m,kxfk/m 1 Received : 30 October
2 GBS OPERATORS OF SCHURER-STANCU TYPE 35 where p m,k x are the fundamental Schurer polynomials. Extensions of the operator 1.1 to the case of bivariate functions were studied in our earlier papers [8], [9] and [10]. In 1968, D.D. Stancu [19] constructed and studied a linear and positive operator depending on two non-negative real parameters α and β which satisfy the condition 0 α β. This operator, denoted by P α,β the polynomial P α,β m f, defined by f P α,β m m, associates to any function f C[0, 1] x =p m,k xf k + α m + β where p m,k x are the fundamental Bernstein polynomials. The operator 1. is known in mathematical literature as the Bernstein-Stancu operator. Extensions of the operator 1. to the case of bivariate functions were constructed by F. Stancu [3] and D. Bărbosu [5], [6], [9]. Considering a given integer p 0 and two real parameters α and β which satisfy the condition 0 α β, in our recent paper [11] was constructed the linear and positive operator S α,β m,p, defined for any f C[0, 1+p] and any m N by x = m+p k + α p m,kxf k=0 m + β Sα,β m,p f The operator 1.3 was called Schurer-Stancu type operator, because for α = β = 0 it reduces to the operator 1.1 and for p = 0, it reduces to the operator 1.. If p =0,α = β = 0, the operator 1.3 is the classical Bernstein operator. Considering two given intergers p 0,q 0 and four real parameters α 1,β 1,α,β satisfying the conditions 0 α 1 β 1 and 0 α β, in the paper [9] we α1,β1,α,β constructed the bivariate operator of Schurer-Stancu type S : C 1 [0, 1+ p] [0, 1+q] C[0, 1] [0, 1], defined for any f C[0, 1+p] [0, 1+q] and any m, n N by Sα 1,β 1,p 1,q 1 f x, y = m+p n+q p mkx p n,j y k=0 j=0 k + α1 f, j + α 4 m + β 1 n + β Some approximation properties of 1.3 were studied in the same paper [9]. Clearly, for p = q = 0 the operator 1.4 reduces to the Stancu bivariate operator, studied by F. Stancu [3] and D. Bărbosu [5]. For α 1 = α = β 1 = β = 0, the operator 1.4 is the bivariate Schurer type operator studied in our earlier paper [10]. The aim of the present paper is to extend the operator 1.4 to the case B- continuous Bögel continuous functions. More exactly, we shall present a GBS Generalized Boolean Sum operator of Schurer-Stancu type and some approximation properties of this operator. The term of B-continuous function was introduced by K. Bögel see [1], [13]. One of the first result concerning the approximation of this kind of functions is due to E. Dobrescu and I. Matei [15]. An important test function theorem, the analogous of the well known Korovkin theorem, for approximation of B-continuous functions using GBS-operators is due to C. Badea, I. Badea and H.H. Gonska []. 3
3 36 D. BĂRBOSU The analogous of first order modulus of smoothness for univariate functions is the mixed modulus of smoothness, introduced by I. Badea [4]. This modulus is used for evaluating the approximation order of B-continuous functions using GBS operators. The analogous of well-known Shisha-Mond theorem [17] for B-continuous functions was established by H.H. Gonska [16], C. Badea and C. Cottin [3].. GBS operators of Schurer-Stancu type Let p 0,q 0 be given integers and let us to denote by C b [0, 1+p] [0, 1+q] the space of real valued functions B-continuous on [0, 1+p] [0, 1+q]. Next, we consider four non-negative parameters α 1,β 1,α,β satisfying the conditions 0 α 1 β 1,0 α β. The parametric extensions of the Schurer-Stancu type operators 1.4 are defined respectively by x y S α1,β1 m,p α,β S n,q f f x, y = m+p p m,kxfk/m, y 5 k=0 x, y = n+q p n,jyfx, j/n 6 j=0 It is easy to see that Sα 1,β 1 x m,p and Sα,β y n,q are linear and positive operator see [9]. They commute on C[0, 1 + p] [0, 1 + q] and their product is the bivariate Schurer-Stancu type operator S α1,β1,α,β : C[0, 1+p] [0, 1+q] C[0, 1] [0, 1], defined for any f C[0, 1+p] [0, 1+q] and any m, n N by S α1,β1,α,β f x, y = m+p f k=0 n+q k + α1 m + β 1, j + α n + β p m,kx p n,j y j=0 In [9] were proved, among others, the following properties of the operator.3. Lemma.1. The operator.3 is linear and positive. Lemma.. If e ij s, t =s i t j i, j N, 0 i + j are the test functions, the operator.3 verifies S α1,β1,α,β e 00 ; x, y = 1 8 S α1,β1,α,β e 10 ; x, y = m + p x + α 1 9 m + β 1 m + β S α1,β1,α,β e 0,1 ; x, y = n + q y + α 10 n + β n + β S α1,β1,α,β 1 { e 0 ; x, y = m + p m + β 1 x +m + px1 x+ mm + p + α 1 x + α 13m + β 1 11 m + β 1 m + β 1 7 S α1,β1,α,β 1 { e 0 ; x, y = n + q n + β y +n + qy1 y+ nn + q + α y + α 3n + β n + β n + β 1
4 GBS OPERATORS OF SCHURER-STANCU TYPE 37 Definition.1. Let Ũ α1,β1,α,β : C b [0, 1+p] [0, 1+q] C b [0, 1] [0, 1] be the boolean sum of.1 and., i.e. Ũ α1,β1,α,β = Sα 1,β 1 x m,p + y Sα,β α1,β1,α,β n,q S 13 The operator.9 will be called GBS operator of Schurer-Stancu type. Lemma.3. The GBS operator of Schurer-Stancu type is defined for any f C b [0, 1+p] [0, 1+q] by α Ũ 1,β 1,α,β f x, y = = m+p k=0 n+q j=0 p m,kx p n,j y { k + α1 f m + p,y f x, j + α n + q + f k + α1 m + p, j + α n + q Proof. The assertion follows by direct computation from.9, taking into account of Lemma. the identity.4. Remark.1. 1 For p = q = 0, the operator.10 is the GBS operator of Stancu type, introduced in our paper [6] For α = β = 0, the operator.10 is the GBS operator of Schurer type, introduced in our paper [8] 3 For α = β =0andp = q = 0, the operator.10 is the GBS operator of Bernstein type, introduced by E. Dobrescu and I. Matei [15]. α Theorem.1. For any f C b [0, 1+p] [0, 1+q] the sequence {Ũ 1,β 1,α,β f converges to f uniformly on [0, 1] [0, 1] as m and n tend to infinity. 14 m,n N S α1,β1,α,β Proof. From Lemma.1 and Lemma. the identity.4 follows that is a linear positive operator, reproducing the constant functions. Taking into account of Lemma. the identities.5,.6,.7 and.8 we get: lim S α1,β1,α,β e 10 ; x, y m,n = x lim S α1,β1,α,β e 01 ; x, y m,n = y lim S α1,β1,α,β e 0 + e 0 ; x, y m,n = x + y, uniformly on [0, 1] [0, 1]. We can apply the test functions theorem due to C. Badea, I. Badea and H.H. Gonska [] and we arrive to desired result. In what follows ω mixed denotes the mixed modulus of smoothness see [4], [3], [16] and we suppose known the variant of Shisha-Mond theorem for B-continuous functions see [3], [6]. Theorem.. For any f C b [0, 1+p] [0, 1+q], in each point x, y [0, 1] [0, 1], the operator.10 verifies α Ũ 1,β 1,α,β f x, y fx, y 4ω mixed δ m,p,α1,β 1,x δ n,q,α,β,y 15
5 38 D. BĂRBOSU where δ 1,m,p,α1,β 1,x = p β 1 m + p + x1 x+ m + β 1 m + β 1 + α 1mp mβ 1 β1 m + β 1 3 x + α 13m + p m + β 3 16 δ,n,q,α,β,y = q β n + q + y1 y+ n + β n + β + α nq nβ β n + β y + α 3n + q n + β 17 Proof. Applying the Shisha-Mond type theorem for B-continuous functions see [3], [15] we get Ũ α 1,β 1,α,β 1+δ 1 1 f x, y L α1,β1,α,β x ; x, y+δ 1 L α1,β1,α,β y ; x, y+ + δ1 1 L α1,β1,α,β x y ; x, y ω mixed δ 1,δ 18 for any δ 1 > 0,δ > 0. Next, taking into account of Lemma. and choosing δ 1 = δ m,p,α1,β 1,x, δ = δ n,q,α,β,y in.15, we arrive to the desired inequality.11. Corollary.3. For any f C b [0, 1+p] [0, 1+q], anyx, y [0, 1] [0, 1], the GBS operator of Schurer-Stancu type verify: α Ũ 1,β 1,α,β f x, y fx, y 4 ω mixed δ 1,δ 19 where δ 1 = max δ m,p,α 1,β x [0,1] 1,x, and β 1,β satisfy.14. δ = max y [0,1] δ n,q,α,β,y 0 Proof. The assertion follows from.11, taking into account that the mixed modulus of smoothness is monotonous increasing with respect the natural order relation from R, i.e. δ 1,δ, δ 1,δ [0,b a] [0,d c], δ 1 <δ 1, δ <δ ω mixed δ 1,δ ω mixed δ 1,δ. Remark.. i The theorem. give us the order of local approximation in each point x, y [0, 1] [0, 1] while Corollary.3 give the order of global approximation of B-continuous function f by Ũ α1,β1,α,β ii Naturally, the inequalities.11 and.16 can be more detailed, depending on the relations between the parameters α 1,β 1,α,β,p,q iii As consequences of Theorem.1 and Theorem., for p = q = 0, we obtain approximation properties of the GBS operator of Stancu type, introduced and studied in [6] iv For α 1 = β 1 =0,α = β = 0, as consequences of Theorem.1 and Theorem., we get approximation properties of the GBS operator of Schurer type, introduced
6 GBS OPERATORS OF SCHURER-STANCU TYPE 39 and studied in [8] v For α 1 = β 1 =0,α = β =0,p = q = 0, we get approximation properties of the GBS operator of Bernstein type, introduced by E. Dobrescu and I. Matei see [15] and studied also by I. Badea see [3] and many others. References [1] O. Agratini, Aproximare prin operatori liniari, Cluj-Napoca, Presa Universitară Clujeană, 000 Romanian. [] C. Badea, I. Badea, H.H. Gonska, A test function theorem and approximation by pseudopolynomials, Bull. Austral. Math. Soc., 34, [3] C. Badea, C. Cottin, Korovkin-type theorems for Generalized Boolean Sum operators, Colloquia Mathematica Societatis Janos Bolyai, 58, Approximation Theory, Kecskemet Hungary, [4] I. Badea, Modul de continuitate în sens Bögel şi unele aplicaţii în aproximarea printr-un operator Bernstein, Studia Univ. Babeş-Bolyai, Ser. Math-Mech, 18, Romanian. [5] D. Bărbosu, Aproximarea funcţiilor de mai multe variabile prin sume booleene de operatori liniari de tip interpolator, Cluj-Napoca, Risoprint, 00 Romanian. [6] D. Bărbosu, Aproximation properties of a bivariate Stancu type operator, Studia Univ. Babeş- Bolyai, Matematica, XLVII4, [7] D. Bărbosu, GBS operators of Bernstein-Schurer type to appear in Matematica, Cluj-Napoca. [8] D. Bărbosu, Bivariate operators of Schurer-Stancu type to appear in Anal. Şt. Univ. Ovidius, Constanţa. [9] D. Bărbosu, Bivariate operators of Bernstein-Schurer type to appear in Rev. Anal. Num. Theor. Approx.. [10] D. Bărbosu, Schurer-Stancu type operators to appear in Studia Univ. Babeş-Bolyai. [11] K. Bögel, Mehrdimensionale Differention von Funktionen mehrer Väränderlicher, J. Reine Angew. Math., 170, [1] K. Bögel, Über die mehrdimensionale Differentiation Integration und beschränkte Variation, J. Reine Angew. Math., 173, [13] F.J. Delvos, W. Schempp, Boolean Methods in Interpolation and Approximation, Harlow, UK: Longman Scientific & Technical [14] E. Dobrescu, I. Matei, Aproximarea prin polinoame de tip Bernstein a funcţiilor bidimensional continue, Anal. Univ. Timişoara, Seria Ştiinţe matematice-fizice, IV, [15] H.H. Gonska, Quantitative approximation in CX, Habilitationsschrift, Universitaät Duisburg [16] O. Shisha, B. Mond, The degree of convergence of linear operators, Acad. Sci. U.S.A., 60, [17] F. Schurer, Linear positive operators in approximation theory, Math. Inst. Techn. Univ. Delft: Report, 196. [18] D.D. Stancu, Approximation of functions by a new class of linear polynomial operators, Rev. Roum. Math. Pures et Appl., 138, [19] D.D. Stancu, Asupra unei generalizări a polinoamelor lui Bernstein, Studia Univ. Babeş- Bolyai, 14, Romanian. [0] D.D. Stancu, Curs şi culegere de probleme de analiză numerică, I, Cluj-Napoca, Lito. Univ. Babeş-Bolyai, 1977 Romanian. [1] D.D. Stancu, Gh. Coman, O. Agratini, R. Trîmbiţaş, Analiză numerică şi teoria aproximării, I, Cluj-Napoca, Presa Universitară Clujeană, 001 Romanian. [] F. Stancu, Aproximarea funcţiilor de două şi mai multe variabile cu ajutorul operatorilor liniari pozitivi, Cluj-Napoca, Ph.D. Thesis, 1984 Romanian. Dan Bărbosu Department of Mathematics and Computer Science Faculty of Sciences North University of Baia Mare Victoriei 76, 4800 Baia Mare, ROMANIA address: dbarbosu@ubm.ro, danbarbosu@yahoo.com
ON THE ORDER OF APPROXIMATION OF FUNCTIONS BY THE BIDIMENSIONAL OPERATORS FAVARD-SZÁSZ-MIRAKYAN
An. Şt. Univ. Ovidius Constanţa Vol. 112, 2003, 163 170 ON THE ORDER OF APPROXIMATION OF FUNCTIONS BY THE BIDIMENSIONAL OPERATORS FAVARD-SZÁSZ-MIRAKYAN Ioana Taşcu and Anca Buie Abstract We will present
More informationCERTAIN CONTRIBUTIONS OF THE ROMANIAN SCHOOL OF NUMERICAL ANALYSIS AND APPROXIMATION THEORY
An. Şt. Univ. Ovidius Constanţa Vol. 13(1), 2005, 115 122 CERTAIN CONTRIBUTIONS OF THE ROMANIAN SCHOOL OF NUMERICAL ANALYSIS AND APPROXIMATION THEORY Andrei Vernescu To Professor Dan Pascali, at his 70
More informationON A CLASS OF LINEAR POSITIVE BIVARIATE OPERATORS OF KING TYPE
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LI, Number 4, December 2006 ON A CLASS OF LINEAR POSITIVE BIVARIATE OPERATORS OF KING TYPE OCTAVIAN AGRATINI Dedicated to Professor Gheorghe Coman at his
More informationVORONOVSKAJA-TYPE THEOREM FOR CERTAIN GBS OPERATORS. Ovidiu T. Pop National College Mihai Eminescu of Satu Mare, Romania
GLASNIK MAEMAIČKI Vol. 43632008, 79 94 VORONOVSKAJA-YPE HEOREM FOR CERAIN GBS OPERAORS Ovidiu. Pop National College Mihai Einescu o Satu Mare, Roania Abstract. In this paper we will deonstrate a Voronovsaja-type
More informationBézier type surfaces. Applied Mathematics & Information Sciences An International Journal. 1. Introduction
Appl. Math. Inf. Sci. 7 No. 2 483-489 203 483 Applied Matheatics & Inforation Sciences An International Journal c 203 NSP Bézier type surfaces Pişcoran Laurian-Ioan Ovidiu T. Pop 2 Bărbosu Dan 3 Technical
More informationThe combined Shepard-Lidstone bivariate operator
Trends and Applications in Constructive Approximation (Eds.) M.G. de Bruin, D.H. Mache & J. Szabados International Series of Numerical Mathematics Vol. 151 c 2005 Birkhäuser Verlag Basel (ISBN 3-7643-7124-2)
More informationPROFESSOR PETRU BLAGA AT HIS 60 TH ANNIVERSARY
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LII, Number 3, September 2007 PROFESSOR PETRU BLAGA AT HIS 60 TH ANNIVERSARY OCTAVIAN AGRATINI AND GHEORGHE COMAN Petru Blaga was born on 7 th September 1947
More informationEQUICONTINUITY AND SINGULARITIES OF FAMILIES OF MONOMIAL MAPPINGS
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LI, Number 3, September 2006 EQUICONTINUITY AND SINGULARITIES OF FAMILIES OF MONOMIAL MAPPINGS WOLFGANG W. BRECKNER and TIBERIU TRIF Dedicated to Professor
More information1994, Phd. in mathematics, Faculty of mathematics and informatics, University of Bucharest.
DUMITRU POPA Date of birth: 21. 07. 1956, com. Cosimbesti, jud. Ialomita. Studies: 1976-1981, Faculty of mathematics and informatics, University of Bucharest. 1994, Phd. in mathematics, Faculty of mathematics
More informationA FIXED POINT PROOF OF THE CONVERGENCE OF A NEWTON-TYPE METHOD
Fixed Point Theory, Volume 7, No. 2, 2006, 235-244 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.htm A FIXED POINT PROOF OF THE CONVERGENCE OF A NEWTON-TYPE METHOD VASILE BERINDE AND MĂDĂLINA PĂCURAR Department
More informationSome Approximation Results For (p, q)-lupaş-schurer Operators
Filomat 3:1 018, 17 9 https://doi.org/10.98/fil180117k Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Some Approimation Results
More informationFixed point theorems for Zamfirescu mappings in metric spaces endowed with a graph
CARPATHIAN J. MATH. 31 2015, No. 3, 297-305 Online version availale at http://carpathian.um.ro Print Edition: ISSN 1584-2851 Online Edition: ISSN 1843-4401 Fixed point theorems for Zamfirescu mappings
More informationFixed point theorems for Ćirić type generalized contractions defined on cyclic representations
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 8 (2015), 1257 1264 Research Article Fixed point theorems for Ćirić type generalized contractions defined on cyclic representations Adrian Magdaş
More informationAn estimation of a generalized divided difference in uniformly convex spaces
An estimation of a generalized divided difference in uniformly convex spaces MIRA-CRISTIANA ANISIU CLUJ-NAPOCA) VALERIU ANISIU CLUJ-NAPOCA) Abstract The rest in some approximation formulae can be expressed
More informationCOMMON FIXED POINT THEOREMS FOR MULTIVALUED OPERATORS ON COMPLETE METRIC SPACES
STUDIA UNIV. BABEŞ BOLYAI MATHEMATICA Volume XLVII Number 1 March 00 COMMON FIXED POINT THEOREMS FOR MULTIVALUED OPERATORS ON COMPLETE METRIC SPACES 1. Introduction The purpose of this paper is to prove
More informationA best approximation property of the generalized spline functions
General Mathematics Vol. 16, No. 4 (2008), 25 33 A best approximation property of the generalized spline functions Adrian Branga Abstract In the introduction of this paper is presented the definition of
More information1968 1, , B.
CURRICULUM VITAE Name: Viorica Mariela Ungureanu Date of Birth: the 4th February 1968 Place of Birth: Tirgu-Jiu, Romania Nationality: Romanian Professional Address: University Constantin Brancusi, Bulevardul
More informationA Structural Theorem of the Generalized Spline Functions 1
General Mathematics Vol. 17, No. 2 (2009), 135 143 A Structural Theorem of the Generalized Spline Functions 1 Adrian Branga Abstract In the introduction of this paper is presented the definition of the
More informationOn a generalization of an approximation operator defined by A. Lupaş 1
General Mathematics Vol. 15, No. 1 (2007), 21 34 On a generalization of an approximation operator defined by A. Lupaş 1 Ulrich Abel and Mircea Ivan Dedicated to Professor Alexandru Lupaş on the ocassion
More informationA GENERALIZATION OF KANTOROVICH OPERATORS AND A SHAPE-PRESERVING PROPERTY OF BERNSTEIN OPERATORS
Bulletin of the Transilvania University of Braşov Vol 5(54, No. 2-212 Series III: Mathematics, Informatics, Physics, 65-68 A GENERALIZATION OF KANTOROVICH OPERATORS AND A SHAPE-PRESERVING PROPERTY OF BERNSTEIN
More informationarxiv: v3 [math.ca] 26 Nov 2015
Some approximation results on Bernstein-Schurer operators defined by p, q-integers Revised arxiv:504.05876v3 math.ca 6 Nov 05 M. Mursaleen, Md. Nasiruzzaman and Ashirbayev Nurgali Department of Mathematics,
More informationON BLEIMANN-BUTZER-HAHN OPERATORS FOR EXPONENTIAL FUNCTIONS ULRICH ABEL AND MIRCEA IVAN
BULL. AUSTRAL. MATH. SOC. VOL. 75 (2007) [409-415] 41A36, 05A19, 05A20 ON BLEIMANN-BUTZER-HAHN OPERATORS FOR EXPONENTIAL FUNCTIONS ULRICH ABEL AND MIRCEA IVAN Some inequalities involving the binomial coefficients
More informationFixed point of ϕ-contraction in metric spaces endowed with a graph
Annals of the University of Craiova, Mathematics and Computer Science Series Volume 374, 2010, Pages 85 92 ISSN: 1223-6934 Fixed point of ϕ-contraction in metric spaces endowed with a graph Florin Bojor
More informationA CLASS OF EVEN DEGREE SPLINES OBTAINED THROUGH A MINIMUM CONDITION
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume XLVIII, Number 3, September 2003 A CLASS OF EVEN DEGREE SPLINES OBTAINED THROUGH A MINIMUM CONDITION GH. MICULA, E. SANTI, AND M. G. CIMORONI Dedicated to
More informationINDICATIVE PROPOSITIONS
An. Şt. Univ. Ovidius Constanţa Vol. 9(1), 2001, 89 94 INDICATIVE PROPOSITIONS Ioan Purdea and Nicolae Both Abstract Two new problems of bivalent propositional logic are proposed here: firstly, to distinguish
More informationBEST APPROXIMATIONS AND ORTHOGONALITIES IN 2k-INNER PRODUCT SPACES. Seong Sik Kim* and Mircea Crâşmăreanu. 1. Introduction
Bull Korean Math Soc 43 (2006), No 2, pp 377 387 BEST APPROXIMATIONS AND ORTHOGONALITIES IN -INNER PRODUCT SPACES Seong Sik Kim* and Mircea Crâşmăreanu Abstract In this paper, some characterizations of
More informationON THE CONVERGENCE OF THE ISHIKAWA ITERATION IN THE CLASS OF QUASI CONTRACTIVE OPERATORS. 1. Introduction
Acta Math. Univ. Comenianae Vol. LXXIII, 1(2004), pp. 119 126 119 ON THE CONVERGENCE OF THE ISHIKAWA ITERATION IN THE CLASS OF QUASI CONTRACTIVE OPERATORS V. BERINDE Abstract. A convergence theorem of
More informationSome Approximation Properties of Szasz-Mirakyan-Bernstein Operators
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol 7, No 4, 04, 49-48 ISSN 307-5543 wwwejpamcom Some Approximation Properties of Szasz-Mirakyan-Bernstein Operators Tuncay Tunç, Ersin Şimşek, Department
More informationPARALLEL NUMERICAL METHODS FOR SOLVING NONLINEAR EQUATIONS
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume XLVI, Number 4, December 2001 PARALLEL NUMERICAL METHODS FOR SOLVING NONLINEAR EQUATIONS IOANA CHIOREAN 1. Introduction The basis for constructing a parallel
More informationSOME PROPERTIES PRESERVED BY WEAK NEARNESS. Adriana Buică
SOME PROPERTIES PRESERVED BY WEAK NEARNESS Adriana Buică Department of Applied Mathematics Babeş-Bolyai University of Cluj-Napoca, 1 Kogalniceanu str., 3400 Romania Abstract: We show that the properties
More informationZygfryd Kominek REMARKS ON THE STABILITY OF SOME QUADRATIC FUNCTIONAL EQUATIONS
Opuscula Mathematica Vol. 8 No. 4 008 To the memory of Professor Andrzej Lasota Zygfryd Kominek REMARKS ON THE STABILITY OF SOME QUADRATIC FUNCTIONAL EQUATIONS Abstract. Stability problems concerning the
More informationOn the efficiency of some optimal quadrature formulas attached to some given quadrature formulas
General Mathematics Vol., No. 3 4 (22, 47 56 On the efficiency of some optimal quadrature formulas attached to some given quadrature formulas Monica Hossu Dedicated to Professor D. D. Stancu on his 75th
More informationFIXED POINTS AND CONTINUITY OF ALMOST CONTRACTIONS
FIXED POINTS AND CONTINUITY OF ALMOST CONTRACTIONS VASILE BERINDE AND MĂDĂLINA PĂCURAR Abstract. Almost contractions form a class of generalized contractions that includes several contractive type mappings
More informationOn the Iyengar Madhava Rao Nanjundiah inequality and its hyperbolic version
Notes on Number Theory and Discrete Mathematics Print ISSN 110 51, Online ISSN 67 875 Vol. 4, 018, No., 14 19 DOI: 10.7546/nntdm.018.4..14-19 On the Iyengar Madhava Rao Nanjundiah inequality and its hyperbolic
More informationTHE THEORY OF A METRICAL FIXED POINT THEOREM: THEORETICAL AND APPLICATIVE RELEVANCES
Fixed Point Theory, Volume 9, No. 2, 2008, 541-559 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html THE THEORY OF A METRICAL FIXED POINT THEOREM: THEORETICAL AND APPLICATIVE RELEVANCES IOAN A. RUS Department
More informationFIXED POINT THEOREMS FOR NONSELF SINGLE-VALUED ALMOST CONTRACTIONS
Fixed Point Theory, 14(2013), No. 2, 301-312 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html FIXED POINT THEOREMS FOR NONSELF SINGLE-VALUED ALMOST CONTRACTIONS VASILE BERINDE AND MĂDĂLINA PĂCURAR Department
More informationRelevant Classes of Weakly Picard Operators
DOI: 10.1515/awutm -2016-0019 Analele Universităţii de Vest, Timişoara Seria Matematică Informatică LIV, 2, (2016), 131 147 Relevant Classes of Weakly Picard Operators Ioan A. Rus Abstract. In this paper
More informationOn the operators defined by Lupaş with some parameters based on q-integers
Mathematics Today Vol.34A April 018 - Special Issue 0-10 ISSN 0976-38, e-issn 455-9601 On the operators defined by Lupaş with some parameters based on q-integers Prashantkumar Patel St. Xavier s College
More informationResearch Article Asymptotic Behaviour of the Iterates of Positive Linear Operators
Abstract and Applied Analysis Volume 2011, Article ID 670509, 11 pages doi:10.1155/2011/670509 Research Article Asymptotic Behaviour of the Iterates of Positive Linear Operators Ioan Gavrea and Mircea
More informationPROFESSOR PETRU BLAGA AT HIS 60 TH ANNIVERSARY
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LII, Number 3, September 2007 PROFESSOR PETRU BLAGA AT HIS 60 TH ANNIVERSARY OCTAVIAN AGRATINI AND GHEORGHE COMAN Petru Blaga was born on 7 th September 1947
More informationA MAXIMUM PRINCIPLE FOR A MULTIOBJECTIVE OPTIMAL CONTROL PROBLEM
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume XLVIII, Number 1, March 23 A MAXIMUM PRINCIPLE FOR A MULTIOBJECTIVE OPTIMAL CONTROL PROBLEM Rezumat. Un principiu de maxim pentru o problemă vectorială de
More informationSOME DUALITY THEOREMS FOR LINEAR-FRACTIONAL PROGRAMMING HAVING THE COEFFICIENTS IN A SUBFIELD K OF REAL NUMBERS
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume XLVI, Number 4, December 2001 SOME DUALITY THEOREMS FOR LINEAR-FRACTIONAL PROGRAMMING HAVING THE COEFFICIENTS IN A SUBFIELD K OF REAL NUMBERS DOINA IONAC
More informationarxiv: v4 [math.ca] 9 May 2012
MILLS RATIO: RECIPROCAL CONVEXITY AND FUNCTIONAL INEQUALITIES Dedicated to my children Boróka Koppány arxiv:.3267v4 [math.ca] 9 May 22 Abstract. This note contains sufficient conditions for the probability
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics NEWER APPLICATIONS OF GENERALIZED MONOTONE SEQUENCES L. LEINDLER Bolyai Institute, University of Szeged, Aradi vértanúk tere 1 H-6720 Szeged, Hungary
More informationBernstein Polynomials and Operator Theory
Result.Math. 53 (2009), 229 236 c 2009 Birkhäuser Verlag Basel/Switzerland 1422-6383/030229-8, published online June 29, 2009 DOI 10.1007/s00025-008-0333-1 Results in Mathematics Bernstein Polynomials
More informationCARISTI TYPE OPERATORS AND APPLICATIONS
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume XLVIII, Number 3, September 2003 Dedicated to Professor Gheorghe Micula at his 60 th anniversary 1. Introduction Caristi s fixed point theorem states that
More informationAPPROXIMATION OF BIVARIATE FUNCTIONS BY OPERATORS OF STANCU HURWITZ TYPE. 1. Introduction
FACTA UNIVERSITATIS NIŠ Ser. Math. Inor. 5, 33 39 APPROXIMATION OF BIVARIATE FUNCTIONS BY OPERATORS OF STANCU HURWITZ TYPE Ioana Taşcu Abstract. The ai o this paper is to introduce and study a linear positive
More informationA FORMULA FOR THE MEAN CURVATURE OF AN IMPLICIT REGULAR SURFACE
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume XLVI, Number 3, September 001 A FORMULA FOR THE MEAN CURVATURE OF AN IMPLICIT REGULAR SURFACE Abstract. In this paper we will ind a ormula or the absolute
More informationEXISTENCE OF STRONG SOLUTIONS OF FULLY NONLINEAR ELLIPTIC EQUATIONS
EXISTENCE OF STRONG SOLUTIONS OF FULLY NONLINEAR ELLIPTIC EQUATIONS Adriana Buică Department of Applied Mathematics Babeş-Bolyai University of Cluj-Napoca, 1 Kogalniceanu str., RO-3400 Romania abuica@math.ubbcluj.ro
More informationarxiv: v1 [math.nt] 2 May 2011
Inequalities for multiplicative arithmetic functions arxiv:1105.0292v1 [math.nt] 2 May 2011 József Sándor Babeş Bolyai University Department of Mathematics Str. Kogălniceanu Nr. 1 400084 Cluj Napoca, Romania
More informationInfinitely many maximal primitive positive clones in a diagonalizable algebra
BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Numbers 2(72) 3(73), 2013, Pages 47 52 ISSN 1024 7696 Infinitely many maximal primitive positive clones in a diagonalizable algebra Andrei
More informationThis condition was introduced by Chandra [1]. Ordonez Cabrera [5] extended the notion of Cesàro uniform integrability
Bull. Korean Math. Soc. 4 (2004), No. 2, pp. 275 282 WEAK LAWS FOR WEIGHTED SUMS OF RANDOM VARIABLES Soo Hak Sung Abstract. Let {a ni, u n i, n } be an array of constants. Let {X ni, u n i, n } be {a ni
More informationGeometry Problem booklet
Geometry Problem booklet Assoc. Prof. Cornel Pintea E-mail: cpintea math.ubbcluj.ro Contents 1 Week 1: Vector algebra 1 1.1 Brief theoretical background. Free vectors..................... 1 1.1.1 Operations
More informationU.P.B. Sci. Bull., Series A, Vol. 74, Iss. 3, 2012 ISSN SCALAR OPERATORS. Mariana ZAMFIR 1, Ioan BACALU 2
U.P.B. ci. Bull., eries A, Vol. 74, Iss. 3, 212 IN 1223-727 A CALAR OPERATOR Mariana ZAMFIR 1, Ioan BACALU 2 În această lucrare studiem o clasă nouă de operatori numiţi -scalari. Aceştia apar în mod natural,
More informationCommentationes Mathematicae Universitatis Carolinae
Commentationes Mathematicae Universitatis Carolinae Bogdan Szal Trigonometric approximation by Nörlund type means in L p -norm Commentationes Mathematicae Universitatis Carolinae, Vol. 5 (29), No. 4, 575--589
More informationExistence and data dependence for multivalued weakly Ćirić-contractive operators
Acta Univ. Sapientiae, Mathematica, 1, 2 (2009) 151 159 Existence and data dependence for multivalued weakly Ćirić-contractive operators Liliana Guran Babeş-Bolyai University, Department of Applied Mathematics,
More informationFIXED POINT THEOREMS OF KRASNOSELSKII TYPE IN A SPACE OF CONTINUOUS FUNCTIONS
Fixed Point Theory, Volume 5, No. 2, 24, 181-195 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.htm FIXED POINT THEOREMS OF KRASNOSELSKII TYPE IN A SPACE OF CONTINUOUS FUNCTIONS CEZAR AVRAMESCU 1 AND CRISTIAN
More informationPublications: Journal Articles
Publications: Over 80 total publications and presentations, including over 46 refereed journal articles, 6 books, over 25 papers, refereed and published in conference proceedings, one submitted work, and
More informationON A COMPOUND APPROXIMATION OPERATOR OF D.D. STANCU TYPE
REVUE D ANALYSE NUMÉRIQUE ET DE THÉORIE DE L APPROXIMATION Toe 35, N o 1, 2006, pp 33 40 ON A COMPOUND APPROXIMATION OPERATOR OF DD STANCU TYPE MARIA CRĂCIUN Abstract In this note we consider a linear
More informationOn some shift invariant integral operators, univariate case
ANNALES POLONICI MATHEMATICI LXI.3 1995) On some shift invariant integral operators, univariate case by George A. Anastassiou Memphis, Tenn.) and Heinz H. Gonska Duisburg) Abstract. In recent papers the
More informationOn an irreducibility criterion of Perron for multivariate polynomials
Bull. Math. Soc. Sci. Math. Roumanie Tome 53(101) No. 3, 2010, 213 217 On an irreducibility criterion of Perron for multivariate polynomials by Nicolae Ciprian Bonciocat Dedicated to the memory of Laurenţiu
More informationA NOTE ON MULTIVALUED MEIR-KEELER TYPE OPERATORS
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LI, Number 4, December 2006 A NOTE ON MULTIVALUED MEIR-KEELER TYPE OPERATORS ADRIAN PETRUŞEL AND GABRIELA PETRUŞEL Dedicated to Professor Gheorghe Coman at
More informationON RANDOM FIXED POINTS IN RANDOM CONVEX STRUCTURES
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LIII, Number 2, June 2008 ON RANDOM FIXED POINTS IN RANDOM CONVEX STRUCTURES ASHOK GANGULY, RAGHVENDRA SINGH CHANDEL, AND RAVINDRA PARSAI Abstract. In this
More informationCATEGORICAL SEQUENCES AND APPLICATIONS
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume XLVII, Number 2, June 2002 CATEGORICAL SEQUENCES AND APPLICATIONS GRAŢIELA CICORTAŞ Abstract. Ralph Fox characterized the Lusternik-Schnirelmann category
More informationSPECIAL FUNCTIONS WITH APPLICATIONS IN NUMERICAL ANALYSIS
BABEŞ-BOLYAI UNIVERSITY CLUJ-NAPOCA FACULTY OF MATHEMATICS AND INFORMATICS ELENA-IULIA STOICA SPECIAL FUNCTIONS WITH APPLICATIONS IN NUMERICAL ANALYSIS ABSTRACT SCIENTIFIC ADVISOR PROF. DR. DR. H. C. DIMITRIE
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics INEQUALITIES FOR GENERAL INTEGRAL MEANS GHEORGHE TOADER AND JOZSEF SÁNDOR Department of Mathematics Technical University Cluj-Napoca, Romania. EMail:
More informationThe equivalence of Picard, Mann and Ishikawa iterations dealing with quasi-contractive operators
Mathematical Communications 10(2005), 81-88 81 The equivalence of Picard, Mann and Ishikawa iterations dealing with quasi-contractive operators Ştefan M. Şoltuz Abstract. We show that the Ishikawa iteration,
More informationMIXED TYPE OF ADDITIVE AND QUINTIC FUNCTIONAL EQUATIONS. Abasalt Bodaghi, Pasupathi Narasimman, Krishnan Ravi, Behrouz Shojaee
Annales Mathematicae Silesianae 29 (205, 35 50 Prace Naukowe Uniwersytetu Śląskiego nr 3332, Katowice DOI: 0.55/amsil-205-0004 MIXED TYPE OF ADDITIVE AND QUINTIC FUNCTIONAL EQUATIONS Abasalt Bodaghi, Pasupathi
More informationSPACES ENDOWED WITH A GRAPH AND APPLICATIONS. Mina Dinarvand. 1. Introduction
MATEMATIČKI VESNIK MATEMATIQKI VESNIK 69, 1 (2017), 23 38 March 2017 research paper originalni nauqni rad FIXED POINT RESULTS FOR (ϕ, ψ)-contractions IN METRIC SPACES ENDOWED WITH A GRAPH AND APPLICATIONS
More informationA GENERALIZATION OF THE REGULARIZATION PROXIMAL POINT METHOD
A GENERALIZATION OF THE REGULARIZATION PROXIMAL POINT METHOD OGANEDITSE A. BOIKANYO AND GHEORGHE MOROŞANU Abstract. This paper deals with the generalized regularization proximal point method which was
More informationPROFESSOR PETRU T. MOCANU ON HIS 70 th BIRTHDAY
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume XLVI, Number 2, June 2001 PROFESSOR PETRU T. MOCANU ON HIS 70 th BIRTHDAY Professor Petru T. Mocanu was born on June 1, 2001 in Brăila, Romania. He attended
More informationINEQUALITIES FOR THE NORM AND THE NUMERICAL RADIUS OF LINEAR OPERATORS IN HILBERT SPACES
INEQUALITIES FOR THE NORM AND THE NUMERICAL RADIUS OF LINEAR OPERATORS IN HILBERT SPACES S.S. DRAGOMIR Abstract. In this paper various inequalities between the operator norm its numerical radius are provided.
More informationON NADLER S MULTI-VALUED CONTRACTION PRINCIPLE IN COMPLETE METRIC SPACES
ISSN 2066-6594 Ann. Acad. Rom. Sci. Ser. Math. Appl. Vol. 10, No. 1/2018 ON NADLER S MULTI-VALUED CONTRACTION PRINCIPLE IN COMPLETE METRIC SPACES Adrian Petruşel Dedicated to Professor Mihail Megan on
More informationSOME PÓLYA-TYPE IRREDUCIBILITY CRITERIA FOR MULTIVARIATE POLYNOMIALS NICOLAE CIPRIAN BONCIOCAT, YANN BUGEAUD, MIHAI CIPU, AND MAURICE MIGNOTTE
SOME PÓLYA-TYPE IRREDUCIBILITY CRITERIA FOR MULTIVARIATE POLYNOMIALS NICOLAE CIPRIAN BONCIOCAT, YANN BUGEAUD, MIHAI CIPU, AND MAURICE MIGNOTTE Abstract. We provide irreducibility criteria for multivariate
More informationarxiv: v1 [math.cv] 7 Jul 2016
UNIVALENCE AND QUASICONFORMAL EXTENSION OF AN INTEGRAL OPERATOR ERHAN DENIZ, STANIS LAWA KANAS, AND HALIT ORHAN arxiv:167.298v1 [math.cv] 7 Jul 216 Abstract. In this paper we give some sufficient conditions
More informationSang-baek Lee*, Jae-hyeong Bae**, and Won-gil Park***
JOURNAL OF THE CHUNGCHEONG MATHEMATICAL SOCIETY Volume 6, No. 4, November 013 http://d.doi.org/10.14403/jcms.013.6.4.671 ON THE HYERS-ULAM STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY Sang-baek Lee*,
More informationOscillation Criteria for Certain nth Order Differential Equations with Deviating Arguments
Journal of Mathematical Analysis Applications 6, 601 6 001) doi:10.1006/jmaa.001.7571, available online at http://www.idealibrary.com on Oscillation Criteria for Certain nth Order Differential Equations
More informationDouble Fourier series, generalized Lipschitz és Zygmund classes
Double Fourier series, generalized Lipschitz és Zygmund classes Summary of the PhD Theses Zoltán Sáfár SUPERVISOR: Ferenc Móricz DSc PROFESSOR EMERITUS UNIVERSITY OF SZEGED FACULTY OF SCIENCE AND INFORMATICS
More informationDiscrete Mathematics
Discrete Mathematics 310 (2010) 109 114 Contents lists available at ScienceDirect Discrete Mathematics journal homepage: www.elsevier.com/locate/disc Total palindrome complexity of finite words Mira-Cristiana
More informationON WEAK CONVERGENCE THEOREM FOR NONSELF I-QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES
BULLETIN OF INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN 1840-4367 Vol. 2(2012), 69-75 Former BULLETIN OF SOCIETY OF MATHEMATICIANS BANJA LUKA ISSN 0354-5792 (o), ISSN 1986-521X (p) ON WEAK CONVERGENCE
More informationHAIYUN ZHOU, RAVI P. AGARWAL, YEOL JE CHO, AND YONG SOO KIM
Georgian Mathematical Journal Volume 9 (2002), Number 3, 591 600 NONEXPANSIVE MAPPINGS AND ITERATIVE METHODS IN UNIFORMLY CONVEX BANACH SPACES HAIYUN ZHOU, RAVI P. AGARWAL, YEOL JE CHO, AND YONG SOO KIM
More informationOn a bivariate interpolation formula
Proc. of the 8th WSEAS Int. Conf. on Mathematical Methods and Computational Techniques in Electrical Engineering, Bucharest, October 16-17, 2006 113 On a bivariate interpolation formula DANA SIMIAN Lucian
More informationPerov s fixed point theorem for multivalued mappings in generalized Kasahara spaces
Stud. Univ. Babeş-Bolyai Math. 56(2011), No. 3, 19 28 Perov s fixed point theorem for multivalued mappings in generalized Kasahara spaces Alexandru-Darius Filip Abstract. In this paper we give some corresponding
More informationPROFESSOR GRIGORE CĂLUGĂREANU AT HIS 60 TH ANNIVERSARY
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LII, Number 2, June 2007 PROFESSOR GRIGORE CĂLUGĂREANU AT HIS 60 TH ANNIVERSARY Grigore Călugăreanu was born on the 20 th of January 1947, in Cluj-Napoca,
More informationA note on a construction of J. F. Feinstein
STUDIA MATHEMATICA 169 (1) (2005) A note on a construction of J. F. Feinstein by M. J. Heath (Nottingham) Abstract. In [6] J. F. Feinstein constructed a compact plane set X such that R(X), the uniform
More informationUNIFORM BOUNDS FOR BESSEL FUNCTIONS
Journal of Applied Analysis Vol. 1, No. 1 (006), pp. 83 91 UNIFORM BOUNDS FOR BESSEL FUNCTIONS I. KRASIKOV Received October 8, 001 and, in revised form, July 6, 004 Abstract. For ν > 1/ and x real we shall
More informationA remark on the proof of Cobzaş-Mustăţa theorem concerning norm preserving extension of convex Lipschitz functions
Stud Univ Babeş-Bolyai Math 57(2012), No 3, 325 329 A remark on the proof of Cobzaş-Mustăţa theorem concerning norm preserving extension of convex Lipschitz functions Iulian Cîmpean Abstract In this paper
More informationLOG-LIKE FUNCTIONS AND UNIFORM DISTRIBUTION MODULO ONE. 1. Introduction and results
uniform distribution theory DOI: 0478/udt-08 003 Unif Distrib Theory 3 (08), no, 93 0 LOG-LIKE FUNCTIONS AND UNIFORM DISTRIBUTION MODULO ONE Martin Rehberg Technische Hochschule Mittelhessen, Friedberg,
More informationNOTE ON A FIXED POINT THEOREM
Fixed Point Theory, Volume 5, No. 1, 2004, 81-85 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.htm NOTE ON A FIXED POINT THEOREM DOREL MIHEŢ West University of Timişoara Faculty of Mathematics Bv. V. Parvan
More informationADJOINTS OF LIPSCHITZ MAPPINGS
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume XLVIII, Number 1, March 2003 ADJOINTS OF LIPSCHITZ MAPPINGS ŞTEFAN COBZAŞ Dedicated to Professor Wolfgang W. Breckner at his 60 th anniversary Abstract. The
More informationRELATION BETWEEN SMALL FUNCTIONS WITH DIFFERENTIAL POLYNOMIALS GENERATED BY MEROMORPHIC SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS
Kragujevac Journal of Mathematics Volume 38(1) (2014), Pages 147 161. RELATION BETWEEN SMALL FUNCTIONS WITH DIFFERENTIAL POLYNOMIALS GENERATED BY MEROMORPHIC SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL
More information2 K cos nkx + K si" nkx) (1.1)
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 71, Number 1, August 1978 ON THE ABSOLUTE CONVERGENCE OF LACUNARY FOURIER SERIES J. R. PATADIA Abstract. Let / G L[ it, -n\ be 27r-periodic. Noble
More informationCRITICAL POINT METHODS IN DEGENERATE ANISOTROPIC PROBLEMS WITH VARIABLE EXPONENT. We are interested in discussing the problem:
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LV, Number 4, December 2010 CRITICAL POINT METHODS IN DEGENERATE ANISOTROPIC PROBLEMS WITH VARIABLE EXPONENT MARIA-MAGDALENA BOUREANU Abstract. We work on
More informationOn (M, N)-convex functions
Notes on Number Theory and Discrete Mathematics ISSN 1310 513 Vol. 1, 015, No. 4, 40 47 On (M, N)-convex functions József Sándor 1 and Edith Egri 1 Babeş Bolyai University, Department of Mathematics, Cluj-Napoca,
More informationTwo-dimensional Total Palindrome Complexity
Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity ISSN 1584-4536, vol 6, 2008, pp. 3 12. Two-dimensional Total Palindrome Complexity Mira-Cristiana Anisiu (Cluj-Napoca)
More informationTransverse vibrations analysis of a beam with degrading hysteretic behavior by using Euler-Bernoulli beam model
DOI: 10.2478/auom-2018-0008 An. Şt. Univ. Ovidius Constanţa Vol. 26(1),2018, 125 139 Transverse vibrations analysis of a beam with degrading hysteretic behavior by using Euler-Bernoulli beam model Ghiocel
More informationarxiv: v1 [cs.dm] 13 Feb 2010
Properties of palindromes in finite words arxiv:1002.2723v1 [cs.dm] 13 Feb 2010 Mira-Cristiana ANISIU Valeriu ANISIU Zoltán KÁSA Abstract We present a method which displays all palindromes of a given length
More informationBetter bounds for k-partitions of graphs
Better bounds for -partitions of graphs Baogang Xu School of Mathematics, Nanjing Normal University 1 Wenyuan Road, Yadong New District, Nanjing, 1006, China Email: baogxu@njnu.edu.cn Xingxing Yu School
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics ON A HYBRID FAMILY OF SUMMATION INTEGRAL TYPE OPERATORS VIJAY GUPTA AND ESRA ERKUŞ School of Applied Sciences Netaji Subhas Institute of Technology
More informationFuzzy Mathematics, Approximation Theory, Optimization, Linear and Quadratic Programming, Functional Analysis.
1. Personal information Name and surname: Lucian COROIANU Date and place of birth: January 26, 1976, Oradea, Romania Marital status: Married, 2 children, 7 and 9 years old Present academic position: Assistant
More information